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# The Discrete Fourier Transform

Fourier analysis is a family of mathematical techniques, all based on decomposing signals into
sinusoids. The discrete Fourier transform (DFT) is the family member used with digitized
signals. This is the first of four chapters on the real DFT, a version of the discrete Fourier
transform that uses real numbers to represent the input and output signals. The complex DFT,
a more advanced technique that uses complex numbers, will be discussed in Chapter 31. In this
chapter we look at the mathematics and algorithms of the Fourier decomposition, the heart of the
DFT.
CHAPTER
The Discrete Fourier Transform
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Fourier analysis is a family of mathematical techniques, all based on decomposing signals into
sinusoids. The discrete Fourier transform (DFT) is the family member used with digitized
signals. This is the first of four chapters on the real DFT , a version of the discrete Fourier
transform that uses real numbers to represent the input and output signals. The complex DFT ,
a more advanced technique that uses complex numbers, will be discussed in Chapter 31. In this
chapter we look at the mathematics and algorithms of the Fourier decomposition, the heart of the
DFT.

The Family of Fourier Transform
Fourier analysis is named after Jean Baptiste Joseph Fourier (1768-1830),
a Fren……

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